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Use the method of elimination through addition to solve the following system of equations.
(1) x/2 + y/5 = 1/2
(2) 3x - y = -8
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x/2 + y/5 = 1/2, (1)
3x - y = -8. (2)
Multiply equation (1) by 10 (both sides) to rid off denominators. You will get
5x + 2y = 5 (3)
instead of (1), and it is good. Now you have the system of two equations
5x + 2y = 5, (3)
3x - y = -8. (2)
Now multiply equation (2) by 2 (both sides) and then add to equation (3).
By doing this, you eliminate the unknown y and get a single equation for the unknown x:
5x + 6x = 5 + 2*(-8), or
11x = -11.
Hence, x = -1.
Now from (2) you have y = 3x + 8 = 3*(-1) + 8 = 5.
The system is solved. The solution is x = -1, y = 5.
